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(b) Find the value of ( 3)f  , (0)f and (1)f .

x 2

g
21. (a) Functions f and g are defined by ( )f x  , x  1 and   x  ax  bx c ,
x  1
,x where a, b and c are constants.

(i) Find  f f , and hence , determine the inverse of f .

2x  2 5x  2
(ii) Find the values of a, b and c if g f   x  2 . .
x   1

2
q
(b) Find the values of q if the function   4f x  x   2  and f 1    5  3 ; x  0 .

2
2
f
22. Given the function   x   p x   3  If f  1   2   2 , find the value of p.

23. The functions f and g are given by   3f x   e  3x and ( )g x  ln(3x  5) .

(a) Find the value of x such that  f g   4x  .

(b) If  f g  1   4b  , find the value of .

2
f
24. Consider the function   x  x  4x  3.
(a) Express   x in the form of x h   2 k , such that x h . Hence, find the value of
f
h.

f
(b) Sketch the graph of   x for x h and explain why f is a one-to-one function. State
f
the range of   x .
(c) Find f  1   x and hence, evaluate f  1   3 .


5 ax
25. Given ( )g x  and ( ) 2h x  x  2 5. Find
2
x
(a) g  1 ( )

2

(b) the value of a so that 2g  1 ( ) h x
)
(
x
(c)
 2x 2 , x  0
26. A piecewise function f is given as ( )f x  
4
x
 x  2 ,    0